Depth First and Breadth First Search - Page 7
       by kirupa  |  13 January 2006

On the previous page, you were able to see the output produced by your search methods in Flash and some tips on implementing this or any other algorithm into your own program.

In this page, I wrap up this tutorial by discussing some positive and negative features of both search algorithms.


Advantages and Disadvantages
If you tried various combination of search results from the Flash example, you can tell that each search method has its advantages and disadvantages. Let's go back to our search tree:

When you use depth first search, what do you think the path between nodes A and C will be? The following is what the path actually will be:

a, b, d, e, f, g, h, j, l, m, k, i, c

Are you surprised at how long the path was even though C is a direct neighbor of A? For further proof, try simulating this in the dfs.fla file from the previous page. What happens if you repeat the same example using the breadth first search example found in bfs.fla?

Likewise, compare the path produced by depth first search and breadth first search when going from A to D. In this case, depth first search produces a better result.

Because of the way both of these algorithms work, you will often miss the forest for the trees. Despite C being just on hop away from its destination, depth first search will avoid it for a long time because the nodes it examines first are those of its neighbors as opposed to nodes on the same depth.

You will find numerous such abnormal behaviors in both methods. This is because both search methods are considered blind searches. They don't know anything about their future or where the target is. The paths the expand are mechanically defined. If a better path exists, they will not take it. If they are taking the wrong path, they won't know it.

For many real-world situations, though, you will not have nicely balanced trees such as what you have seen in this tutorial. Ideally, you would let these algorithms loose on graphs containing hundreds of thousands of nodes with a myriad of edges. After all, if we could solve these ourselves, we would have no need to have a computer do it for us.

With large graphs, you may run into cycles or loops. If you really want to see our depth first search algorithm fail, simply add an edge between nodes D and node A:

You will eventually crash the system because depth first search will simply keep adding in the values a, b, and d continuously without ever breaking out of the loop.

Another problem is, what if the left side of your tree has millions of nodes, but your destination is close to the origin on the right side of the tree. Depth first would waste numerous cycles exploring the left side before ever reaching the right side.

Breadth first search does not suffer from the same loop problems because it moves horizontally across each depth. Breadth first will always find a solution regardless of what type of search tree you have unless there are infinite nodes.

Memory is often a limiting factor. Having millions or billions of nodes, as is the case with searching the web, both depth first and breadth first searches are at the mercy of the computers powering them. Fortunately, there are many better, more complicated search methods that address all of the problems of both depth and breadth first searches AND produce far better results.

I shall cover other search methods at a later time, but hopefully this tutorial provided a good groundwork on how to think about solving complicated problems using a computer, informally stating a solution in a computer-understandable way, converting our informal solution into actual code, and disseminating the results. It just so happens you also learned about two popular search algorithms in the process.


If you have a question about this or any other topic, the easiest thing is to drop by our forums where a bunch of the friendliest people you'll ever run into will be happy to help you out!

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